You are running the latest version of Firefox (10.0.2) and sync is builtin (nothing to install anymore).

However, your useragent is showing as Firefox 3.5.5...to fix do the following:

Type about:config in the URL bar and hit Enter

If you see the warning, you can confirm that you want to access that page.

Filter = general.useragent.

Right-click the preferences that are bold, one line at a time, and select Reset.

Then restart Firefox

You are running the latest version of Firefox (10.0.2) and sync is builtin (nothing to install anymore).
However, your useragent is showing as Firefox 3.5.5...to fix do the following:
* Type about:config in the URL bar and hit Enter
* If you see the warning, you can confirm that you want to access that page.
* Filter = general.useragent.
* Right-click the preferences that are bold, one line at a time, and select Reset.
* Then restart Firefox

No, Sync is no longer supported for Firefox 3.5 and 3.6 versions and the Sync extension has been redrawn.<br />
You need to update to current Firefox 10 to get full sync support.
See:
*https://support.mozilla.org/kb/Finding+your+Firefox+version
*https://support.mozilla.org/kb/Websites+or+add-ons+incorrectly+report+incompatible+browser

Even though you said you are running Firefox 10.0.2 your User Agent is shown as:
Mozilla/5.0 (Windows; U; Windows NT 6.0; en-US; rv:1.9.1.5) Gecko/20091102 Firefox/3.5.5 (.NET CLR 3.5.30729)
If you are in fact running Firefox 10.0.2 then see the "Other causes" section of
[[Websites incorrectly report that Firefox is outdated or incompatible]] and reset
all '''useragent''' preferences from the "about:config" page.